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Learn: Differentiation
AQA 7357 A Level Mathematics
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Welcome!Today we'll explore differentiation, an essential topic in calculus. It's all about rates of change and slopes of curves!
What is Differentiation?Differentiation is a mathematical process used to find the rate at which one quantity changes with respect to another. For example, it helps us calculate how fast a car is accelerating or how steep a hill is at a specific point.
Gradient of a CurveTo find the gradient (slope) of a curve at a specific point, we use differentiation. The gradient represents the steepness or rate of change of the curve at that point.
Quick check: What does differentiation calculate?
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Basic Differentiation RulesThere are simple rules for differentiating functions. For example, if f(x) = xn, then f'(x) = nxn-1. This is known as the power rule.
If f(x) = x3, then f'(x) = {{blank0}}x{{blank1}}.
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Applications of DifferentiationDifferentiation is used to find maxima and minima, calculate rates of change, and solve optimisation problems. For example, businesses use it to maximise profit or minimise costs.
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Review Time!Great work! You've learned about differentiation, gradients, and its applications. Now let's test your understanding with a few questions.
Which of the following are true about differentiation? (Select all that apply)
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Match the items on the left with their correct pairs on the right
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What is the derivative of f(x) = 7x2?
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You're doing great!You've mastered the basics of differentiation. Keep practising to get even better at solving problems involving rates of change and optimisation.
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